Abstract
Understanding the behavior of sliding charge density waves (CDWs) in the presence of an electric field is a challenging problem because one must understand how the competition between randomness and interactions affects the properties of a nonlinear dynamical system with many degrees of freedom. These lectures describe two aspects of this problem. The first concerns the dynamical generation of defects in CDWs when they are subjected to a uniform electric field. It is shown that amplitude defects, or phase slips, must always occur in the presence of a uniform nonzero electric field for a sample of infinite size. The defect density for real CDWs is estimated and it is shown that phase slips could be present in substantial numbers in even high quality samples. The experimental situation is then addressed, and it is seen that phase slips contribute in an important way to the dynamical response of the CDW in almost all samples. The applicability of this work to other systems such as Wigner crystals and flux lattices in type-II superconductors is discussed. The second concerns the dynamical selection of atypical metastable states when the CDW is subjected to repeated identical voltage pulses. The experimental manifestation of this selection is a synchronization of the CDW current response with the end of the driving pulse.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
For a review of CDWs, see, e.g., G. Grüner, Rev. Mod. Phys. 60, 1129 (1988).
H. Fukuyama and P.A. Lee, Phys. Rev. B17, 535 (1978)
P.A. Lee and T.M. Rice, Phys. Rev. B19, 3970 (1979).
L. Sneddon, M.C. Cross, and D.S. Fisher, Phys. Rev. Lett. 49, 292 (1982).
The relation between the equations of motion used here and the original CDW equations of motion is discussed in L. Pietronero and S. Strassler, Phys. Rev. B 28, 5683 (1983)
P.B. Littlewood in Charge-Density Waves in Solids, ed. L.P. Gor’kov and G. Gruner (Elsevier, Amsterdam, 1989)
D.S. Fisher, Phys. Rev. B. 31, 1396 (1985).
See, e.g., D.S. Fisher, Phys. Rev. B 31, 1396 (1985)
S.N. Coppersmith and D.S. Fisher, Phys. Rev. A 38, 6338 (1988)
P. Sibani and P.B. Littlewood, Phys. Rev. Lett. 64, 1305 (1990)
P.B. Littlewood and C.M. Vanna, Phys. Rev. B 36, 480 (1987)
J.B. Sokoloff, Phys. Rev. B 31, 2270 (1985)
A. Middleton and D.S. Fisher, Phys. Rev. Lett. 66, 92 (1991)
C.R. Myers and J.P. Sethna, unpublished; O. Narayan and D.S. Fisher, Phys. Rev. B46, 11520 (1992).
S.N. Coppersmith, Phys. Rev. Lett. 65, 1044 (1990).
S.N. Coppersmith and A.J. Millis, Phys. Rev. B44, 7799 (1991).
S.N. Coppersmith, Phys. Rev. B44, 2887 (1991).
L. Mihaly, M. Crommie, and G. Gruner, Europhys. Lett. 4, 103 (1987).
Similar calculations have been done in the context of oscillator entrainment; see, H. Sakaguchi et al., Prog. Theor. Phys. 77, 1005 (1987)
S.H. Strogatz and R.E. Mirollo, J. Phys. A 21, L699 (1988)
S.H. Strogatz and R.E. Mirollo, Physica D 31, 143 (1988).
The argument involving very rare fluctuations is related to arguments used for random magnets; R.B. Griffiths, Phys. Rev. Left. 23, 17 (1969)
M. Randeria, J. Sethna, and R. Palmer, Phys. Rev. Lett. 54, 1321 (1985).
The methods used are similar to those used to calculate the density of states of impurity states in the band tails of disordered semiconductors; see B.I. Halperin and M. Lax, Phys. Rev. 148, 722 (1966)
J. Zittartz and J.S. Langer, Phys. Rev. 148, 741 (1966).
Y. Imry and S.-k. Ma, Phys. Rev. Lett. 35, 1399 (1975).
This result can be demonstrated simply for a simplified model.[8]
M. Randeria, J. Sethna, and R. Palmer, Phys. Rev. Lett. 54, 1321 (1985).
D. DiCarlo, E. Sweetland, M. Sutton, J.D. Brock, and R.E. Thome, Phys. Rev. Lett. 70, 845 (1993).
See, e.g., P. Segransan et al., Phys. Rev. Lett. 56, 1854 (1986).
See, e.g., S. Bhattacharya, M.J. Higgins, and J. P. Stokes, Phys. Rev. Lett. 63, 1508 (1989).
J. McCarten, D.A. DiCarlo, M.P. Maher, T.L. Adelman, and R.E. Thome, Phys. Rev. B46, 4456 (1992).
M.J. Higgins, A.A. Middleton and S. Bhattacharya, Bull. A.P.S. 38, 383 (1993), and preprint.
S. Bhattacharya, J.P. Stokes, M.O. Robbins, and R. A. Klemm, Phys. Rev. Lett. 54, 2453 (1985)
M.O. Robbins, J.P. Stokes, and S. Bhattacharya, Phys. Rev. Lett. 55, 2822 (1985).
M.S. Sherwin and A. Zettl, Phys. Rev. B32, 5536 (1985).
P.B. Littlewood, Phys. Rev. B33, 6694 (1986).
A.A. Middleton, Ph. D. Thesis, Princeton University (1990)
A.A. Middleton, Phys. Rev. Lett. 68, 670 (1992).
M.P. Maher, T.L. Adelman, J. McCarten, D.A. DiCarlo, and R.E. Thorne, Phys. Rev. B43, 9968 (1991).
S. Bhattacharya et al., Phys. Rev. Lett. 59, 1849 (1987)
G.L. Link and G. Mozurkewich, Solid State Commun. 65, 15 (1988).
See, e.g., A. Schmid and W. Hauger, J. Low Temp. Phys. 11, 667 (1973).
The arguments in this paper do not imply an instability of a model including long-wavelength deformations only in systems with unscreened long-ranged interactions if the impurity potential is weak enough. However, this situation is significantly more complicated than that described by the phase deformation model because in such a system shear and rotation cost much less energy than compression, and one must account for this when considering the dynamics of the long-wavelength modes.
In this volume Henrik Jensen describes numerical simulations demonstrating that plastic flow is important in two-dimensional systems. O. Pla and F. Nori (private communication) have also obtained good numerical evidence that inhomogeneous conduction occurs in two dimensions for a model of flux lines with short-range interactions.
S. Bhattacharya and M. Higgins, preprint.
See, e.g., B.G.A. Norman, P.B. Littlewood, and A.J. Millis, Phys. Rev. B46, 3920 (1992).
Y.P. Li, T. Sajoto, L.W. Engel, D.C. Tsui, M. Shayegan, Phys. Rev. Lett. 67, 1630 (1991).
S.N. Coppersmith and P.B. Littlewood, Phys. Rev. B 36, 311 (1987)
See also C. Tang et al., Phys. Rev. Lett. 58, 1161 (1987).
R.M. Fleming and L.F. Schneemeyer, Phys. Rev. B 33, 2930 (1986).
S.E. Brown, G. Gruner, and L. Mihaly, Solid State Commun. 57, 165 (1986).
It can be shown that Eqs. (2) need not have unbounded strains when F(t) takes the form of repeated pulses. In addition the synchronization occurs even if the CDW has broken up into several pieces. Thus, studying Eqs. (2) is adequate to understand the effect.
S.N. Coppersmith, Physics Letters A 125, 473 (1987).
S.N. Coppersmith, Phys. Rev. A 36, 3375 (1987).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Coppersmith, S.N. (1993). Charge Density Waves, Phase Slips, and Instabilities. In: Riste, T., Sherrington, D. (eds) Phase Transitions and Relaxation in Systems with Competing Energy Scales. NATO ASI Series, vol 415. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1908-5_14
Download citation
DOI: https://doi.org/10.1007/978-94-011-1908-5_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4843-9
Online ISBN: 978-94-011-1908-5
eBook Packages: Springer Book Archive